Daubechies Wavelet

The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function (called the father wavelet) which generates an orthogonal multiresolution analysis.

Daubechies小波，基于Ingrid Daubechies的工作，是一组定义离散小波变换的正交小波，并且以给定支撑的最大消失矩数量为特征。对于此类的每个小波类型，都有一个尺度函数（称为父小波），它生成正交多分辨率分析。

In general the Daubechies wavelets are chosen to have the highest number A of vanishing moments, (this does not imply the best smoothness) for given support width 2A - 1.[1] There are two naming schemes in use, DN using the length or number of taps, and dbA referring to the number of vanishing moments. So D4 and db2 are the same wavelet transform.

一般来说，对于给定的支持宽度2A-1，Daubechies小波被选择为具有最高数目的消失矩A（这并不意味着最佳平滑度）。[1]在使用中有两种命名方案，DN使用抽头的长度或数量，dbA使用消失矩的数量。NTS。因此，D4和DB2是相同的小波变换。

Among the 2^A−1 possible solutions of the algebraic equations for the moment and orthogonality conditions, the one is chosen whose scaling filter has extremal phase. The wavelet transform is also easy to put into practice using the fast wavelet transform. Daubechies wavelets are widely used in solving a broad range of problems, e.g. self-similarity properties of a signal or fractal problems, signal discontinuities, etc.

在矩和正交性条件下的代数方程的2^A-1可能解中，选择具有极值相位的尺度滤波器。小波变换也易于应用于快速小波变换。Daubechies小波在解决信号自相似性、分形问题、信号不连续性等问题中得到了广泛的应用。

The Daubechies wavelets are not defined in terms of the resulting scaling and wavelet functions; in fact, they are not possible to write down in closed form. The graphs below are generated using the cascade algorithm, a numeric technique consisting of simply inverse-transforming [1 0 0 0 0 ... ] an appropriate number of times.

Daubechies小波不是根据得到的缩放和小波函数定义的; 事实上，它们不可能以封闭形式写下来。下面的图是使用级联算法生成的，这是一种由简单的逆变换[1 0 0 0.…适当的次数。